Question

A stunt cyclist rides on the interior of a cylinder 12 m in radius. The coefficient of static friction between the tires and the wall is 0.68. Find the value of the minimum speed for the cyclist to perform the stunt.

a) 8.72 m/s
b) 10.24 m/s
c) 12.50 m/s
d) 15.18 m/s

Answer 1

The minimum speed for the stunt cyclist to perform the stunt is 15.18 m/s.

Step-by-step explanation:

To find the minimum speed for the stunt cyclist to perform the stunt, we need to consider the centripetal force required to keep the cyclist from sliding down the wall. The force of friction between the tires and the wall provides this centripetal force. The maximum force of static friction is given by the equation:

fs = μN

Where μ is the coefficient of static friction and N is the normal force, which is equal to the weight of the cyclist (mg) in this case. The centripetal force required is given by the equation:

fc = mv²/r

To find the minimum speed, we can equate fs and fc and solve for v:

μmg = mv²/r

Simplifying the equation, we get:

v = √(μgr)

Substituting the values given in the question, we have:

v = √(0.68*9.8*12)

Solving for v, we get 15.18 m/s. Therefore, option d) 15.18 m/s is the correct answer.